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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.analysis.interpolation;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.NoDataException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.NonMonotonicSequenceException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.util.MathArrays;<a name="line.22"></a>
<FONT color="green">023</FONT>    <a name="line.23"></a>
<FONT color="green">024</FONT>    /**<a name="line.24"></a>
<FONT color="green">025</FONT>     * Generates a tricubic interpolating function.<a name="line.25"></a>
<FONT color="green">026</FONT>     *<a name="line.26"></a>
<FONT color="green">027</FONT>     * @since 2.2<a name="line.27"></a>
<FONT color="green">028</FONT>     * @version $Id: TricubicSplineInterpolator.java 1379904 2012-09-01 23:54:52Z erans $<a name="line.28"></a>
<FONT color="green">029</FONT>     */<a name="line.29"></a>
<FONT color="green">030</FONT>    public class TricubicSplineInterpolator<a name="line.30"></a>
<FONT color="green">031</FONT>        implements TrivariateGridInterpolator {<a name="line.31"></a>
<FONT color="green">032</FONT>        /**<a name="line.32"></a>
<FONT color="green">033</FONT>         * {@inheritDoc}<a name="line.33"></a>
<FONT color="green">034</FONT>         */<a name="line.34"></a>
<FONT color="green">035</FONT>        public TricubicSplineInterpolatingFunction interpolate(final double[] xval,<a name="line.35"></a>
<FONT color="green">036</FONT>                                                               final double[] yval,<a name="line.36"></a>
<FONT color="green">037</FONT>                                                               final double[] zval,<a name="line.37"></a>
<FONT color="green">038</FONT>                                                               final double[][][] fval)<a name="line.38"></a>
<FONT color="green">039</FONT>            throws NoDataException,<a name="line.39"></a>
<FONT color="green">040</FONT>                   DimensionMismatchException,<a name="line.40"></a>
<FONT color="green">041</FONT>                   NonMonotonicSequenceException {<a name="line.41"></a>
<FONT color="green">042</FONT>            if (xval.length == 0 || yval.length == 0 || zval.length == 0 || fval.length == 0) {<a name="line.42"></a>
<FONT color="green">043</FONT>                throw new NoDataException();<a name="line.43"></a>
<FONT color="green">044</FONT>            }<a name="line.44"></a>
<FONT color="green">045</FONT>            if (xval.length != fval.length) {<a name="line.45"></a>
<FONT color="green">046</FONT>                throw new DimensionMismatchException(xval.length, fval.length);<a name="line.46"></a>
<FONT color="green">047</FONT>            }<a name="line.47"></a>
<FONT color="green">048</FONT>    <a name="line.48"></a>
<FONT color="green">049</FONT>            MathArrays.checkOrder(xval);<a name="line.49"></a>
<FONT color="green">050</FONT>            MathArrays.checkOrder(yval);<a name="line.50"></a>
<FONT color="green">051</FONT>            MathArrays.checkOrder(zval);<a name="line.51"></a>
<FONT color="green">052</FONT>    <a name="line.52"></a>
<FONT color="green">053</FONT>            final int xLen = xval.length;<a name="line.53"></a>
<FONT color="green">054</FONT>            final int yLen = yval.length;<a name="line.54"></a>
<FONT color="green">055</FONT>            final int zLen = zval.length;<a name="line.55"></a>
<FONT color="green">056</FONT>    <a name="line.56"></a>
<FONT color="green">057</FONT>            // Samples, re-ordered as (z, x, y) and (y, z, x) tuplets<a name="line.57"></a>
<FONT color="green">058</FONT>            // fvalXY[k][i][j] = f(xval[i], yval[j], zval[k])<a name="line.58"></a>
<FONT color="green">059</FONT>            // fvalZX[j][k][i] = f(xval[i], yval[j], zval[k])<a name="line.59"></a>
<FONT color="green">060</FONT>            final double[][][] fvalXY = new double[zLen][xLen][yLen];<a name="line.60"></a>
<FONT color="green">061</FONT>            final double[][][] fvalZX = new double[yLen][zLen][xLen];<a name="line.61"></a>
<FONT color="green">062</FONT>            for (int i = 0; i &lt; xLen; i++) {<a name="line.62"></a>
<FONT color="green">063</FONT>                if (fval[i].length != yLen) {<a name="line.63"></a>
<FONT color="green">064</FONT>                    throw new DimensionMismatchException(fval[i].length, yLen);<a name="line.64"></a>
<FONT color="green">065</FONT>                }<a name="line.65"></a>
<FONT color="green">066</FONT>    <a name="line.66"></a>
<FONT color="green">067</FONT>                for (int j = 0; j &lt; yLen; j++) {<a name="line.67"></a>
<FONT color="green">068</FONT>                    if (fval[i][j].length != zLen) {<a name="line.68"></a>
<FONT color="green">069</FONT>                        throw new DimensionMismatchException(fval[i][j].length, zLen);<a name="line.69"></a>
<FONT color="green">070</FONT>                    }<a name="line.70"></a>
<FONT color="green">071</FONT>    <a name="line.71"></a>
<FONT color="green">072</FONT>                    for (int k = 0; k &lt; zLen; k++) {<a name="line.72"></a>
<FONT color="green">073</FONT>                        final double v = fval[i][j][k];<a name="line.73"></a>
<FONT color="green">074</FONT>                        fvalXY[k][i][j] = v;<a name="line.74"></a>
<FONT color="green">075</FONT>                        fvalZX[j][k][i] = v;<a name="line.75"></a>
<FONT color="green">076</FONT>                    }<a name="line.76"></a>
<FONT color="green">077</FONT>                }<a name="line.77"></a>
<FONT color="green">078</FONT>            }<a name="line.78"></a>
<FONT color="green">079</FONT>    <a name="line.79"></a>
<FONT color="green">080</FONT>            final BicubicSplineInterpolator bsi = new BicubicSplineInterpolator();<a name="line.80"></a>
<FONT color="green">081</FONT>    <a name="line.81"></a>
<FONT color="green">082</FONT>            // For each line x[i] (0 &lt;= i &lt; xLen), construct a 2D spline in y and z<a name="line.82"></a>
<FONT color="green">083</FONT>            final BicubicSplineInterpolatingFunction[] xSplineYZ<a name="line.83"></a>
<FONT color="green">084</FONT>                = new BicubicSplineInterpolatingFunction[xLen];<a name="line.84"></a>
<FONT color="green">085</FONT>            for (int i = 0; i &lt; xLen; i++) {<a name="line.85"></a>
<FONT color="green">086</FONT>                xSplineYZ[i] = bsi.interpolate(yval, zval, fval[i]);<a name="line.86"></a>
<FONT color="green">087</FONT>            }<a name="line.87"></a>
<FONT color="green">088</FONT>    <a name="line.88"></a>
<FONT color="green">089</FONT>            // For each line y[j] (0 &lt;= j &lt; yLen), construct a 2D spline in z and x<a name="line.89"></a>
<FONT color="green">090</FONT>            final BicubicSplineInterpolatingFunction[] ySplineZX<a name="line.90"></a>
<FONT color="green">091</FONT>                = new BicubicSplineInterpolatingFunction[yLen];<a name="line.91"></a>
<FONT color="green">092</FONT>            for (int j = 0; j &lt; yLen; j++) {<a name="line.92"></a>
<FONT color="green">093</FONT>                ySplineZX[j] = bsi.interpolate(zval, xval, fvalZX[j]);<a name="line.93"></a>
<FONT color="green">094</FONT>            }<a name="line.94"></a>
<FONT color="green">095</FONT>    <a name="line.95"></a>
<FONT color="green">096</FONT>            // For each line z[k] (0 &lt;= k &lt; zLen), construct a 2D spline in x and y<a name="line.96"></a>
<FONT color="green">097</FONT>            final BicubicSplineInterpolatingFunction[] zSplineXY<a name="line.97"></a>
<FONT color="green">098</FONT>                = new BicubicSplineInterpolatingFunction[zLen];<a name="line.98"></a>
<FONT color="green">099</FONT>            for (int k = 0; k &lt; zLen; k++) {<a name="line.99"></a>
<FONT color="green">100</FONT>                zSplineXY[k] = bsi.interpolate(xval, yval, fvalXY[k]);<a name="line.100"></a>
<FONT color="green">101</FONT>            }<a name="line.101"></a>
<FONT color="green">102</FONT>    <a name="line.102"></a>
<FONT color="green">103</FONT>            // Partial derivatives wrt x and wrt y<a name="line.103"></a>
<FONT color="green">104</FONT>            final double[][][] dFdX = new double[xLen][yLen][zLen];<a name="line.104"></a>
<FONT color="green">105</FONT>            final double[][][] dFdY = new double[xLen][yLen][zLen];<a name="line.105"></a>
<FONT color="green">106</FONT>            final double[][][] d2FdXdY = new double[xLen][yLen][zLen];<a name="line.106"></a>
<FONT color="green">107</FONT>            for (int k = 0; k &lt; zLen; k++) {<a name="line.107"></a>
<FONT color="green">108</FONT>                final BicubicSplineInterpolatingFunction f = zSplineXY[k];<a name="line.108"></a>
<FONT color="green">109</FONT>                for (int i = 0; i &lt; xLen; i++) {<a name="line.109"></a>
<FONT color="green">110</FONT>                    final double x = xval[i];<a name="line.110"></a>
<FONT color="green">111</FONT>                    for (int j = 0; j &lt; yLen; j++) {<a name="line.111"></a>
<FONT color="green">112</FONT>                        final double y = yval[j];<a name="line.112"></a>
<FONT color="green">113</FONT>                        dFdX[i][j][k] = f.partialDerivativeX(x, y);<a name="line.113"></a>
<FONT color="green">114</FONT>                        dFdY[i][j][k] = f.partialDerivativeY(x, y);<a name="line.114"></a>
<FONT color="green">115</FONT>                        d2FdXdY[i][j][k] = f.partialDerivativeXY(x, y);<a name="line.115"></a>
<FONT color="green">116</FONT>                    }<a name="line.116"></a>
<FONT color="green">117</FONT>                }<a name="line.117"></a>
<FONT color="green">118</FONT>            }<a name="line.118"></a>
<FONT color="green">119</FONT>    <a name="line.119"></a>
<FONT color="green">120</FONT>            // Partial derivatives wrt y and wrt z<a name="line.120"></a>
<FONT color="green">121</FONT>            final double[][][] dFdZ = new double[xLen][yLen][zLen];<a name="line.121"></a>
<FONT color="green">122</FONT>            final double[][][] d2FdYdZ = new double[xLen][yLen][zLen];<a name="line.122"></a>
<FONT color="green">123</FONT>            for (int i = 0; i &lt; xLen; i++) {<a name="line.123"></a>
<FONT color="green">124</FONT>                final BicubicSplineInterpolatingFunction f = xSplineYZ[i];<a name="line.124"></a>
<FONT color="green">125</FONT>                for (int j = 0; j &lt; yLen; j++) {<a name="line.125"></a>
<FONT color="green">126</FONT>                    final double y = yval[j];<a name="line.126"></a>
<FONT color="green">127</FONT>                    for (int k = 0; k &lt; zLen; k++) {<a name="line.127"></a>
<FONT color="green">128</FONT>                        final double z = zval[k];<a name="line.128"></a>
<FONT color="green">129</FONT>                        dFdZ[i][j][k] = f.partialDerivativeY(y, z);<a name="line.129"></a>
<FONT color="green">130</FONT>                        d2FdYdZ[i][j][k] = f.partialDerivativeXY(y, z);<a name="line.130"></a>
<FONT color="green">131</FONT>                    }<a name="line.131"></a>
<FONT color="green">132</FONT>                }<a name="line.132"></a>
<FONT color="green">133</FONT>            }<a name="line.133"></a>
<FONT color="green">134</FONT>    <a name="line.134"></a>
<FONT color="green">135</FONT>            // Partial derivatives wrt x and wrt z<a name="line.135"></a>
<FONT color="green">136</FONT>            final double[][][] d2FdZdX = new double[xLen][yLen][zLen];<a name="line.136"></a>
<FONT color="green">137</FONT>            for (int j = 0; j &lt; yLen; j++) {<a name="line.137"></a>
<FONT color="green">138</FONT>                final BicubicSplineInterpolatingFunction f = ySplineZX[j];<a name="line.138"></a>
<FONT color="green">139</FONT>                for (int k = 0; k &lt; zLen; k++) {<a name="line.139"></a>
<FONT color="green">140</FONT>                    final double z = zval[k];<a name="line.140"></a>
<FONT color="green">141</FONT>                    for (int i = 0; i &lt; xLen; i++) {<a name="line.141"></a>
<FONT color="green">142</FONT>                        final double x = xval[i];<a name="line.142"></a>
<FONT color="green">143</FONT>                        d2FdZdX[i][j][k] = f.partialDerivativeXY(z, x);<a name="line.143"></a>
<FONT color="green">144</FONT>                    }<a name="line.144"></a>
<FONT color="green">145</FONT>                }<a name="line.145"></a>
<FONT color="green">146</FONT>            }<a name="line.146"></a>
<FONT color="green">147</FONT>    <a name="line.147"></a>
<FONT color="green">148</FONT>            // Third partial cross-derivatives<a name="line.148"></a>
<FONT color="green">149</FONT>            final double[][][] d3FdXdYdZ = new double[xLen][yLen][zLen];<a name="line.149"></a>
<FONT color="green">150</FONT>            for (int i = 0; i &lt; xLen ; i++) {<a name="line.150"></a>
<FONT color="green">151</FONT>                final int nI = nextIndex(i, xLen);<a name="line.151"></a>
<FONT color="green">152</FONT>                final int pI = previousIndex(i);<a name="line.152"></a>
<FONT color="green">153</FONT>                for (int j = 0; j &lt; yLen; j++) {<a name="line.153"></a>
<FONT color="green">154</FONT>                    final int nJ = nextIndex(j, yLen);<a name="line.154"></a>
<FONT color="green">155</FONT>                    final int pJ = previousIndex(j);<a name="line.155"></a>
<FONT color="green">156</FONT>                    for (int k = 0; k &lt; zLen; k++) {<a name="line.156"></a>
<FONT color="green">157</FONT>                        final int nK = nextIndex(k, zLen);<a name="line.157"></a>
<FONT color="green">158</FONT>                        final int pK = previousIndex(k);<a name="line.158"></a>
<FONT color="green">159</FONT>    <a name="line.159"></a>
<FONT color="green">160</FONT>                        // XXX Not sure about this formula<a name="line.160"></a>
<FONT color="green">161</FONT>                        d3FdXdYdZ[i][j][k] = (fval[nI][nJ][nK] - fval[nI][pJ][nK] -<a name="line.161"></a>
<FONT color="green">162</FONT>                                              fval[pI][nJ][nK] + fval[pI][pJ][nK] -<a name="line.162"></a>
<FONT color="green">163</FONT>                                              fval[nI][nJ][pK] + fval[nI][pJ][pK] +<a name="line.163"></a>
<FONT color="green">164</FONT>                                              fval[pI][nJ][pK] - fval[pI][pJ][pK]) /<a name="line.164"></a>
<FONT color="green">165</FONT>                            ((xval[nI] - xval[pI]) * (yval[nJ] - yval[pJ]) * (zval[nK] - zval[pK])) ;<a name="line.165"></a>
<FONT color="green">166</FONT>                    }<a name="line.166"></a>
<FONT color="green">167</FONT>                }<a name="line.167"></a>
<FONT color="green">168</FONT>            }<a name="line.168"></a>
<FONT color="green">169</FONT>    <a name="line.169"></a>
<FONT color="green">170</FONT>            // Create the interpolating splines<a name="line.170"></a>
<FONT color="green">171</FONT>            return new TricubicSplineInterpolatingFunction(xval, yval, zval, fval,<a name="line.171"></a>
<FONT color="green">172</FONT>                                                           dFdX, dFdY, dFdZ,<a name="line.172"></a>
<FONT color="green">173</FONT>                                                           d2FdXdY, d2FdZdX, d2FdYdZ,<a name="line.173"></a>
<FONT color="green">174</FONT>                                                           d3FdXdYdZ);<a name="line.174"></a>
<FONT color="green">175</FONT>        }<a name="line.175"></a>
<FONT color="green">176</FONT>    <a name="line.176"></a>
<FONT color="green">177</FONT>        /**<a name="line.177"></a>
<FONT color="green">178</FONT>         * Compute the next index of an array, clipping if necessary.<a name="line.178"></a>
<FONT color="green">179</FONT>         * It is assumed (but not checked) that {@code i} is larger than or equal to 0}.<a name="line.179"></a>
<FONT color="green">180</FONT>         *<a name="line.180"></a>
<FONT color="green">181</FONT>         * @param i Index<a name="line.181"></a>
<FONT color="green">182</FONT>         * @param max Upper limit of the array<a name="line.182"></a>
<FONT color="green">183</FONT>         * @return the next index<a name="line.183"></a>
<FONT color="green">184</FONT>         */<a name="line.184"></a>
<FONT color="green">185</FONT>        private int nextIndex(int i, int max) {<a name="line.185"></a>
<FONT color="green">186</FONT>            final int index = i + 1;<a name="line.186"></a>
<FONT color="green">187</FONT>            return index &lt; max ? index : index - 1;<a name="line.187"></a>
<FONT color="green">188</FONT>        }<a name="line.188"></a>
<FONT color="green">189</FONT>        /**<a name="line.189"></a>
<FONT color="green">190</FONT>         * Compute the previous index of an array, clipping if necessary.<a name="line.190"></a>
<FONT color="green">191</FONT>         * It is assumed (but not checked) that {@code i} is smaller than the size of the array.<a name="line.191"></a>
<FONT color="green">192</FONT>         *<a name="line.192"></a>
<FONT color="green">193</FONT>         * @param i Index<a name="line.193"></a>
<FONT color="green">194</FONT>         * @return the previous index<a name="line.194"></a>
<FONT color="green">195</FONT>         */<a name="line.195"></a>
<FONT color="green">196</FONT>        private int previousIndex(int i) {<a name="line.196"></a>
<FONT color="green">197</FONT>            final int index = i - 1;<a name="line.197"></a>
<FONT color="green">198</FONT>            return index &gt;= 0 ? index : 0;<a name="line.198"></a>
<FONT color="green">199</FONT>        }<a name="line.199"></a>
<FONT color="green">200</FONT>    }<a name="line.200"></a>




























































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